where \(S_{*}\)  is the source function. For this source function, we assume local thermal equilibrium, \(S_{*}=aT^{4}\) ,
where \(T\)  is the gas temperature and \(a\)  is the radiation constant. For the equation of state, the gas pressure is given by the ideal gas law, \(p = R_{\rm G}\rho T/\mu \) , where \(\mu \)  is the mean molecular weight and \(R_{\rm G}\)  is the gas constant. To close the system of equations, we use the flux-limited diffusion approximation [1]} for the radiative flux:
\({\textbf {F}}_{0} = - {{\lambda _{\rm f} c}\over {\rho (\kappa + \sigma )}} \nabla {E}_{0}.\) 
